Course overview

Are you curious about how advanced techniques in mathematical modelling are used? Do you want to learn about insights from the latest mathematical research? Perhaps you are keen to apply this learning to a real-life situation with a placement year as part of your degree.

During this MMath you will cover these topics, learning from dedicated mathematicians. Our degree gives you the chance to learn more about the exciting research our academics are working on, whilst equipping you with the knowledge and skills to carry out your own research.

You'll develop your skills in problem solving and analysis. The course will also enable you to enhance and develop your transferable skills in project work, group study and presentations, then apply them in the workplace during your year in industry.

There's a range of specialised modules across all branches of mathematics, based upon our diverse research interests. Our academics are working on problems that span:

  • medicine, biotechnology and food security
  • epidemic modelling
  • fluid mechanics, with applications in industry and biology
  • statistical machine learning
  • algebra and number theory
  • mathematical finance

Year in industry

The industry placement enables you to take what you've learned and apply it to real projects in a professional working environment. The placement year can provide you with a source of income and can even lead to a job offer before you've graduated.

About mathematics at the University of Nottingham

The first year of this accredited degree gives you a flavour of the different areas of mathematics on offer. You will cover topics spanning applied mathematics, pure mathematics, statistics and probability. You will work individually and in groups to solve real-world problems using advanced theories and techniques. It helps you to decide what you enjoy and if there are areas in which you want to specialise.

Later topics include:

  • abstract mathematical structures
  • ordinary and partial differential equations
  • probabilistic and statistical models
  • mathematical finance
  • quantum mechanics and relativity

Putting your maths into practice

There are lots of opportunities to apply your knowledge in a real-world context, by working together with other students and lecturers to tackle complex problems from industry and academia.

We work closely with our industry partners and alumni to ensure the course is matched to employer needs so you can enter the workplace confident in the skills and knowledge you've gained.

Why choose this course?

Industry experience

improve your employability with a year spent working in industry

Opportunity to network

make potential employer contacts

Attend guest lectures

join talks and workshops run by our Industrial Advisory Group and alumni

Transferable skills

in group work, presentations and projects

Paid research projects

gain research experience through a summer research project

Wide module choice

guided by our specialist research areas


students in higher years help with first-year topics and support you to settle in

Peer-Assisted Study Support programme

Entry requirements

All candidates are considered on an individual basis and we accept a broad range of qualifications. The entrance requirements below apply to 2023 entry.

UK entry requirements
A level A*AA/AAA/A*AB

Please note: Applicants whose backgrounds or personal circumstances have impacted their academic performance may receive a reduced offer. Please see our contextual admissions policy for more information.

Required subjects

At least A in A level mathematics. Required grades depend on whether A/AS level further mathematics is offered.

IB score IB 36; 6 in maths at Higher Level. If you're studying the International Baccalaureate we require Higher Level Maths Analysis and Approaches. We do not accept 'Applications and Interpretations'.

A level

Standard offer

A*AA including A* Mathematics


AAA including Mathematics and Further Mathematics


AAA including Mathematics, plus A in AS Further Mathematics


A*AB including A*A in Mathematics and Further Mathematics

The following A levels are not accepted:

  • General Studies
  • Critical Thinking
  • Citizenship Studies
  • Thinking Skills
  • Global Perspectives and Research


English 4 (C) (or equivalent)

University admissions tests

STEP/MAT/TMUA is not required but may be taken into consideration when offered.

Contextual offers

A Levels - AAB including A in Mathematics or Further Mathematics

This type of offer is given to students who meet our contextual admissions or elite athlete criteria.

Find out more about contextual offers at University of Nottingham

Alternative qualifications

In all cases we require applicants to have at least the equivalent of A level Mathematics, so we typically only accept alternative qualifications when combined with an appropriate grade in A level Mathematics.

Foundation progression options

If you don't meet our entry requirements there is the option to study the Engineering and Physical Sciences Foundation Programme. If you satisfy the progression requirements, you can progress to any of our mathematics courses.

There is a course for UK students and one for EU/international students.

Other foundation year programmes are considered individually, but you must have studied maths at an advanced level (up to A-level standard).

Mature Students

At the University of Nottingham, we have a valuable community of mature students and we appreciate their contribution to the wider student population. You can find lots of useful information on the mature students webpage.

Learning and assessment

How you will learn

You will broaden and deepen your knowledge of mathematical ideas and techniques using a wide variety of different methods of study.

In both academia and the wider world of work, mathematics has become a collaborative discipline, and our degree programme takes this into account. As well as more traditional individual study methods, where you work on challenging mathematical problems, you will also collaborate with other students in group problem solving sessions. You will write about your work in reports and present your findings to your study group.

Teaching methods

  • Computer labs
  • Lectures
  • Tutorials
  • Problem classes
  • Seminars
  • Workshops
  • Placements

How you will be assessed

Year 1

Two thirds of the first year is assessed by examination, whilst the remaining marks are gained from coursework, computing assignments and small-scale group projects.

Years 2,3 and 5 (fourth year spent on placement)

Subsequent years will be assessed using a combination of examinations, coursework, computing assignments, group projects and presentations. The specific combination of learning activities will depend on your choice of modules and will be aligned with the topics covered.

The first year is a qualifying year but does not count towards your final degree classification. In year two the assessments will account for 20% of your final mark with years three and five accounting for 40% each. In the fifth year you will do an assessed oral presentation as part of the final year dissertation.

Students require 55% at the first attempt in the second year to progress on this programme. Students who do not achieve this will automatically be transferred to BSc Mathematics with a Year in Industry

You will be given a copy of our marking criteria which provides guidance on how your work is assessed. Your work will be marked in a timely manner and you will have regular opportunities to give and receive feedback on your progress with your tutor and lecturers.

Placement year assessment

The year in industry will be assessed by you being required to prepare a final report and poster of your experience and taking part in a placements fair arranged by the school.

Assessment methods

  • Coursework
  • Group project
  • Poster presentation
  • Research project
  • Written exam
  • Presentation

Contact time and study hours

The majority of modules are worth 10 or 20 credits. You will study modules totalling 120 credits in each year. As a guide one credit equates to approximately 10 hours of work. During the first year, you will typically spend approximately:

  • 12 hours a week in lectures
  • 4 hours a week in problem classes
  • 1 hour each week in tutorials with your personal tutor
  • 1 hour a week in computing workshops across the Autumn and Spring terms
  • 1 hour each fortnight in student-led academic mentoring Peer-Assisted Study Support (PASS)

You can attend optional drop-in sessions each week up to a maximum of three hours and the remaining time will be spent in independent study.

In later years, you are likely to spend approximately 12 hours per week in lectures subject to your module selection.

In your first year you will meet with your personal tutor every week during term time. In small groups of 5-6 students, you'll run through core topics and practice working together in a group to solve problems and communicate mathematics effectively.

All of our modules are delivered by lecturers or professors. PhD students sometimes support problem classes and computing workshops in their areas of expertise. Lectures in the first two years often include at least 200 students but class sizes are much more variable in the third year subject to module selection.

Study abroad

You may choose to spend a semester abroad as part of the degree.

Benefits of studying abroad

  • Explore a new culture
  • A reduced tuition fee of up to 30% for the year in which you spend a semester abroad
  • Improve your communication skills, confidence and independence

Countries you could go to:

  • Australia
  • Canada
  • China (teaching is in English)
  • France
  • Germany
  • Italy
  • New Zealand
  • Singapore (teaching is in English)
  • Spain
  • USA

To study abroad you need to achieve a 60% minimum average mark in your degree, during the year before you travel. A good academic reference and personal statement should be provided as part of the application process.

If you choose to spend a semester abroad through the University-wide exchange programme, the marks gained will count back to your Nottingham degree programme.

Year in industry

The year in industry will be supported by a named placement tutor, through a combination of telephone and/or video-conferencing calls and site visits. The placement year will be assessed through short reflective reports on your work experience, a final report and your participation in a Mathematics with Industry Fair early in the subsequent academic year.

The year does not have to be spent in a mathematics-related role. The following opportunities have been advertised to students previously:

  • Office for National Statistics
  • East Midlands Special Ops
  • National Crime Agency Cyber unit
  • Abbott Diabetes Care
  • Schroders (Luxembourg)


The optional module Communicating Mathematics involves a placement in a local school as a teaching assistant. The placement allows you to gain authentic experience of teaching mathematics, whilst undertaking research to develop your teaching practice and understanding of mathematics education theory.

Study Abroad and the Year in Industry are subject to students meeting minimum academic requirements. Opportunities may change at any time for a number of reasons, including curriculum developments, changes to arrangements with partner universities, travel restrictions or other circumstances outside of the university’s control. Every effort will be made to update information as quickly as possible should a change occur.


You will study the following core mathematics modules during your first year.

Through these core modules you will gain foundational knowledge and skills to pursue advanced topics in any area of mathematics in subsequent years.

Core modules

Analysis and Calculus

Calculus provides the basic, underpinning mathematics for much of modern technology, from the design of chemical reactors and high-speed trains, to models for gene networks and space missions.

The basic ideas that underpin calculus are functions and limits. To study these rigorously you need to learn about the tools of mathematical analysis. In addition to differential equations and the calculus of functions of one or more variables and their differentiation, integration and analysis, you will learn the basics of logic and how to construct rigorous proofs.

Applied Mathematics

You’ll learn how to construct and analyse differential equations that model real-world systems. Applications that you’ll learn about include systems governed by Newton’s laws of motion, such as sets of interacting particles and the orbits of planets, as well as models of population dynamics. You will also be introduced to the mathematical basis of concepts such as work and energy.

Pure Mathematics

Pure mathematics at university is typically very different to the pure mathematics you've learnt at school or college.

In this module, you'll use the language of sets, functions and relations to study abstract mathematical ideas. You will also learn how to construct mathematical proofs. Topics that you will learn about include:

  • set theory
  • prime numbers
  • symmetry and groups
  • rings, fields and integer
  • polynomial arithmetic
Linear Algebra

Linear algebra underpins many areas of modern mathematics. The basic objects that you will study in this module are vectors, matrices and linear transformations. Topics covered include:

  • vector geometry
  • matrix algebra
  • vector spaces
  • linear systems of equations
  • eigenvalues and eigenvectors
  • inner product spaces.

The mathematical tools that you study in this module are fundamental to many mathematical, statistical, and computational models of the real world.

Probability 1

Probability theory allows us to assess risk when calculating insurance premiums. It can help when making investment decisions. It can be used to estimate the impact that government policy will have on climate change or the spread of disease. 

You will study the theory and practice of discrete and continuous probability, including topics such as:

  • Bayes’ theorem
  • multivariate random variables
  • probability distributions
  • the central limit theorem
Programming for Mathematics

There is no area of modern mathematics that does not use computational methods to make progress on problems with which the human brain is unable to cope due to the volume of calculations required.

Scientific computation underpins many technological developments in all sectors of the economy. You'll learn how to write code for mathematical applications using Python.

Python is a freely available, widely-used computer language. No previous computing knowledge will be assumed. It will be used throughout your degree programme.

Statistics 1

Statistics is concerned with methods for collecting, organising, summarising, presenting and analysing data. It enables us to draw valid conclusions and make reasonable decisions based on statistical analysis. It can be used to answer a diverse range of questions in areas such as the pharmaceuticals industry, economic planning and finance. 

The module covers statistical inference, you'll learn how to analyse, interpret and report data. Topics that you’ll learn about include:

  • point estimators and confidence intervals
  • hypothesis testing
  • linear regression
  • goodness-of-fit tests
The above is a sample of the typical modules we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Modules (including methods of assessment) may change or be updated, or modules may be cancelled, over the duration of the course due to a number of reasons such as curriculum developments or staffing changes. Please refer to the module catalogue for information on available modules. This content was last updated on Tuesday 25 October 2022.

You will spend one third of your year studying core mathematics modules. For the remainder of your time, you will choose from a range of optional modules across the three main mathematical subject areas (applied mathematics, pure mathematics, statistics). You will also have the option to choose some modules from outside of mathematics.

During this year you will benefit from modules informed and developed alongside alumni and employers, ensuring they are topical and relevant for future careers.

Core modules

Differential Equations

This module introduces various analytical methods for the solution of ordinary and partial differential equations.

You will begin by studying asymptotic techniques, which can be used when the equations involve a small parameter, which is often the case. We will also study some aspects of dynamical systems theory, which has wide applicability to models of real world problems.

Real and Complex Analysis

This module will further develop your understanding of the tools of real and complex analysis. This provides you with a solid foundation for subsequent modules in metric and topological spaces, relativity, and numerical analysis.

You’ll study topics such as:

  • the Bolzano-Weierstrass Theorem
  • norms, sequences and series of functions
  • differentiability
  • the Riemann integral

You will also learn about functions of complex variables and study topics including, analyticity, Laurent series, contour integrals and residue calculus and its applications.

Vector Calculus

This module teaches you the mathematical foundations of multidimensional differential and integral calculus of scalar and vector functions. This provides essential background for later study involving mathematical modelling with differential equations, such as fluid dynamics and mathematical physics. You will learn about vector differential operators, the divergence theorem and Stokes’ theorem, as well as meeting various curvilinear coordinate systems.

Optional modules


By studying this module, you’ll explore the abstract mathematical structures of different types of groups, including rings. Topics that you’ll study include:

  • permutations
  • Abelian groups
  • quotient groups
  • ring homomorphisms
  • polynomial rings
Mathematical Physics

This module teaches you how Newtonian mechanics can be developed into the more powerful formulations due to Lagrange and Hamilton. You will also be introduced to the basic structure of quantum mechanics.

The module provides the foundation for a wide range of more advanced modules in mathematical physics.

Modelling with Differential Equations

This module will provide you with tools to develop and analyse linear and nonlinear mathematical models based on ordinary and partial differential equations. You will also meet the fundamental mathematical concepts required to model the flow of liquids and gases. This will enable you to apply the resulting theory to model physical situations.

Number Theory

Number theory is a branch of pure mathematics that primarily studies the integers, and has applications, for example, in cryptography.

Topics that you will study include:

  • Diophantine equations
  • congruence equations
  • Fermat’s little theorem
Probability 2

This module will develop your understanding of probability theory and random variables from Probability 1. There's particular attention paid to continuous random variables.

Fundamental concepts relating to probability will be discussed in detail, including limit theorems and the multivariate normal distribution. You will then progress onto more advanced topics such as transition matrices, one-dimensional random walks and absorption probabilities.

Scientific Computation

Most mathematical problems cannot be solved analytically or would take too long to solve by hand. Instead, computational algorithms must be used. 

Scientific Computation teaches you about algorithms for approximating functions, derivatives, and integrals, and for solving many types of equation.

Statistics 2

The first part of this module provides you with an introduction to statistical concepts and methods. The second part introduces a wide range of techniques used in a variety of quantitative subjects. The key concepts of inference including estimation and hypothesis testing will be described, as well as practical data analysis and assessment of model adequacy.

Research internships

During your second year, you may want to apply to do one of the school's research internships. This involves working with an academic member of staff for 8-10 weeks over the summer.

It provides insight into the latest mathematical thinking and an opportunity to get a flavour for what a research career might be like. This is helpful if you are considering future masters or PhD study.

The above is a sample of the typical modules we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Modules (including methods of assessment) may change or be updated, or modules may be cancelled, over the duration of the course due to a number of reasons such as curriculum developments or staffing changes. Please refer to the module catalogue for information on available modules. This content was last updated on

You must take the group project module. The compulsory group project allows you to consolidate your mathematical knowledge and understanding whilst gaining experience of working collaboratively to solve complex problems. Completion of this project provides you with excellent preparation for your fourth year dissertation.

At least half your optional modules must be from one of the following areas:

  • applied mathematics
  • pure mathematics
  • probability and statistics

You will also have the option to choose some modules from outside mathematics if you wish.

Core modules

Mathematics Group Projects

This module involves the application of mathematics to a variety of practical, open-ended problems - typical of those that mathematicians encounter in industry and commerce.

Specific projects are tackled through workshops and student-led group activities. The real-life nature of the problems requires you to develop skills in model development and refinement, report writing and teamwork. There are various streams within the module, for example:

  • Pure Mathematics
  • Applied Mathematics
  • Data Analysis
  • Mathematical Physics

This ensures that you can work in the area that you find most interesting.

Optional modules

Advanced Quantum Theory

In this module you will apply the quantum mechanics that you learned in Year 2 to more general problems. New topics will be introduced such as the quantum theory of the hydrogen atom and aspects of angular momentum such as spin.

Applied Statistical Modelling

During this module you will build on your theoretical knowledge of statistical inference by a practical implementation of the generalised linear model. You will progress to enhance your understanding of statistical methodology including the analysis of discrete and survival data. You will also be trained in the use of a high-level statistical computer program.

Classical and Quantum Dynamics

The module introduces and explores methods, concepts and paradigm models for classical and quantum mechanical dynamics. We explore how classical concepts enter quantum mechanics, and how they can be used to find approximate semi-classical solutions.

Coding and Cryptography

This module provides an introduction to coding theory in particular to error-correcting codes and their uses and applications. You’ll learn cryptography, including classical mono- and polyalphabetic ciphers.  There will also be a focus on modern public key cryptography and digital signatures, their uses and applications.

Communicating Mathematics

This is an excellent opportunity to gain first-hand experience of being involved with providing mathematical education. You will work in a local school alongside practising mathematics teachers in a classroom environment and improve your skills at communicating maths.

Typically, you will work within a class (or classes) for half a day a week for about sixteen weeks. You will be given a range of responsibilities, from classroom assistant to leading a self-originated mathematical activity or project.

The assessment is carried out in a variety of ways: an on-going reflective log, contribution to reflective seminar, oral presentation and a final written report.

Differential Equations

You will be introduced to various analytical methods for the solution of ordinary and partial differential equations. We will begin by studying asymptotic techniques, which can be used when the equations involve a small parameter, which is often the case.

We will also study some aspects of dynamical systems theory, which has wide applicability to models in real world problems.

Discrete Mathematics and Graph Theory

In this module, a graph consists of vertices and edges, each edge joining two vertices. Graph theory has become increasingly important recently through its connections with computer science and its ability to model many practical situations.

Topics covered include:

  • paths and cycles
  • the resolution of Euler’s Königsberg Bridge Problem
  • Hamiltonian cycles and many others
Elliptic Curves

Elliptic curves are useful tools in many areas of number theory and can be used in cryptography. You'll  study topics including:

  • basic notions of projective geometry
  • plane algebraic curves including elliptic curves
  • addition of points on elliptic curves
  • results on the group of rational points on an elliptic curve
  • properties of elliptic curves and their applications

The module provides an introduction to electromagnetism and the electrodynamics of charged particles. You will meet Maxwell’s equations and learn how they describe a wide variety of phenomena, including electrostatic fields and electromagnetic waves.

Fluid Dynamics

You will extend your understanding of fluid flow by introducing the concept of viscosity and studying the fundamental governing equations for the motion of liquids and gases.

Methods for solution of these equations are introduced, including exact solutions and approximate solutions valid for thin layers. A further aim is to apply the theory to model fluid dynamical problems of physical relevance.

Further Number Theory

Number theory concerns the solution of polynomial equations in whole numbers, or fractions. We will establish the basic properties of the Riemann zeta-function to find out how evenly the prime numbers are distributed.

This module will also present several methods to solve Diophantine equations including analytical methods using zeta-functions and Dirichlet series, theta functions and their applications to arithmetic problems. We will also cover an introduction to more general modular forms.

Game Theory

Game theory is relevant to many branches of mathematics (and computing); the emphasis here is primarily algorithmic. The module starts with an investigation into normal-form games, including strategic dominance, Nash equilibria, and the Prisoner’s Dilemma. 

We look at tree-searching, including alpha-beta pruning, the ‘killer’ heuristic and its relatives. It then turns to the mathematical theory of games, exploring the connection between numbers and games, including Sprague-Grundy theory and the reduction of impartial games to Nim.

Group Theory

This module builds on the basic ideas of group theory. It covers a number of key results such as:

  • the simplicity of the alternating groups
  • the Sylow theorems (of fundamental importance in abstract group theory)
  • the classification of finitely generated Abelian groups (required in algebraic number theory, combinatorial group theory and elsewhere).

Other topics to be covered are group actions, used to prove the Sylow theorems, and series for groups, including the notion of solvable groups.

Linear Analysis

You will study an introduction to the ideas of functional analysis with an emphasis on Hilbert spaces and operators on them. Many concepts from linear algebra in finite dimensional vector spaces, for example, writing a vector in terms of a basis, eigenvalues of a linear map, diagonalization, have generalisations in the setting of infinite dimensional spaces.

This makes this theory a powerful tool with many applications in pure and applied mathematics.

Mathematical Finance

You will explore the concepts of discrete time Markov chains to understand how they used. We will also provide an introduction to probabilistic and stochastic modelling of investment strategies, and for the pricing of financial derivatives in risky markets.

You will gain well-rounded knowledge of contemporary issues which are of importance in research and workplace applications.

Mathematical Medicine and Biology

Mathematics can be usefully applied to a wide range of applications in medicine and biology.

Without assuming any prior biological knowledge, this module describes how mathematics helps us understand topics such as:

  • population dynamics
  • biological oscillations
  • pattern formation
  • nonlinear growth phenomena

There is considerable emphasis on model building and development.

Metric and Topological Spaces

A metric space generalises the concept of distance familiar from Euclidean space. It provides a notion of continuity for functions between quite general spaces. The module covers:

  • metric spaces
  • topological spaces
  • compactness
  • separation properties like Hausdorffness and normality
  • Urysohn’s lemma
  • quotient and product topologies, and connectedness

Finally, Borel sets and measurable spaces are introduced.

Multivariate Analysis

This module is concerned with the analysis of multivariate data, in which the response is a vector of random variables rather than a single random variable. A theme running through the module is that of dimension reduction.

Key topics to be covered include:

  • principal components analysis
  • modelling and inference for multivariate data
  • classification of observation vectors into sub-populations using a training sample
  • canonical correlation analysis
  • factor analysis
  • methods of clustering
  • multidimensional scaling

In this module a variety of techniques of mathematical optimisation will be covered including Lagrangian methods for optimisation, simplex algorithm linear programming and dynamic programming.

These techniques have a wide range of applications to real world problems, in which a process or system needs to be made to perform optimally.


You will be introduced to Einstein’s theory of general and special relativity. The relativistic laws of mechanics will be described within a unified framework of space and time. You’ll learn how to compare other theories against this work and you’ll be able to explain exciting new phenomena that occur in relativity.

Rings and Modules

Commutative rings and modules over them are the fundamental objects of what is often referred to as commutative algebra. Key examples of commutative rings are polynomials in one variable over a field and number rings such as the usual integers or the Gaussian integers. There are many close parallels between these two types of rings, for example the similarities between the prime factorization of integers and the factorization of polynomials into irreducibles.

In this module, these ideas are extended and generalized to cover polynomials in several variables and power series, and algebraic numbers.

Scientific Computation and Numerical Analysis

You'll learn how to use numerical techniques for determining the approximate solution of ordinary and partial differential equations where a solution cannot be found through analytical methods alone. You will also cover topics in numerical linear algebra, discovering how to solve very large systems of equations and find their eigenvalues and eigenvectors using a computer.

Statistical Inference

This module is concerned with the two main theories of statistical inference, namely classical (frequentist) inference and Bayesian inference.

You will explore the following topics in detail:

  • sufficiency
  • estimating equations
  • likelihood ratio tests
  • best-unbiased estimators

There is special emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma.

Stochastic Models

This module will develop your knowledge of discrete-time Markov chains by applying them to a range of stochastic models. You will be introduced to Poisson and birth-and-death processes. You will then move onto more extensive studies of epidemic models and queuing models, with introductions to component and system reliability.

The above is a sample of the typical modules we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Modules (including methods of assessment) may change or be updated, or modules may be cancelled, over the duration of the course due to a number of reasons such as curriculum developments or staffing changes. Please refer to the module catalogue for information on available modules. This content was last updated on

You will spend this year on an industry placement.

You will be supported by a placement tutor in securing a position and they will keep in touch during the year to see how you are getting on. They will also help you in preparing a report about your experience on your return to Nottingham for your final year.

On return to university for your final year, you will choose from a wide range of advanced optional modules. You must also write a dissertation, which accounts for one third of your final year. This gives you a taster what it is like to conduct your own research project, under expert supervision.

You will specialise in one of the three main subject areas, and there is also the option to choose some modules from outside mathematics if you wish.

Core modules

Mathematics Dissertation

This module will consist of individual, self-directed, but supervised, study of an appropriate area of mathematics during both semesters.

A list of possible topics will be supplied by the school and you will choose a topic of interest to you. You will be asked to produce a substantial piece of work, assessed by an interim report, an oral presentation and a dissertation.

Optional modules

Advanced Financial Mathematics

You will develop your knowledge and skills relevant to the mathematical modelling of investment and finance. Also, research experience will be broadened by undertaking some independent reading, computer simulations, group work and summarising the material in a project report.

Advanced Techniques for Differential Equations

The development of techniques for the study of nonlinear differential equations is a major research activity to which members of the department here at Nottingham, have made important contributions.

The module covers a number of state-of-the-art methods, for example:

  • Green’s function methods for the solution of linear partial differential equations
  • characteristic methods
  • classification and regularization of nonlinear partial differentiation equations
  • bifurcation theory

These methods will be illustrated by applications in the biological and physical sciences.

Algebraic Number Theory

This module presents the fundamental features of algebraic number theory, the theory in which numbers are viewed from an algebraic point of view. Numbers are often treated as elements of rings, fields and modules, and properties of numbers are reformulated in terms of the relevant algebraic structures.

This approach leads to understanding of certain arithmetical properties of numbers (in particular, integers) from a new point of view.

Black Holes

You’ll systematically study black holes and their properties, including astrophysical processes, horizons and singularities. You’ll have an introduction to black hole radiation to give you an insight into problems of research interest. You’ll gain knowledge to help you begin research into general relativity.

Combinatorial Group Theory

This module is largely concerned with infinite groups, especially free groups, although their role in describing and understanding finite groups is emphasized. Following the basic definitions of free groups and group presentations, the fundamental Nielson-Schreier Theorem is covered in some detail.

You will also learn methods for manipulating group presentations, and using them to read off properties of a given group.

Computational Applied Mathematics

This module introduces computational methods for solving problems in applied mathematics. You will develop knowledge and understanding to design, justify and implement relevant computational techniques and methodologies.

Computational Statistics

This module explores how computers allow the easy implementation of standard, but computationally intensive, statistical methods. You will explore their use in the solution of non-standard analytically intractable problems by innovative numerical methods. The material builds on the theory of the module to cover several topics that form the basis of some current research areas in computational statistics.

Particular topics to be covered include a selection from simulation methods such as:

  • Markov chain
  • Monte Carlo methods
  • the bootstrap
  • nonparametric statistics
  • statistical image analysis
  • wavelets
Differential Geometry

By studying this module, you’ll be equipped with the tools and knowledge to extend your understanding of general relativity. You’ll explore more abstract and powerful concepts using examples of curved space-times such as Lie groups and manifolds among others.

Financial Mathematics

The first part of the module introduces the no-arbitrage pricing principle and financial instruments such as forward and futures contracts, bonds and swaps, and options.

The second part of the module considers the pricing and hedging of options and discrete-time, discrete-space stochastic processes.

The final part of the module focuses on the Black-Scholes formula for pricing European options and also introduces the Wiener process, Ito integrals and stochastic differential equations.

Introduction to Quantum Information Science

This module gives a mathematical introduction to quantum information theory. The aim is to provide you with a background in quantum information science. This will help with your further independent learning and allow you to understand the scope and nature of current research topics.

Quantum Field Theory

In this year-long module you’ll be introduced to the study of the quantum dynamics of relativistic particles. You’ll learn about the quantum description of electrons, photons and other elementary particles, leading to an understanding of the standard model of particle physics.

Scientific Computation and C++

The purpose of this module is to introduce you to the concepts of scientific programming using the object-oriented language C++ It is used for applications arising in the mathematical modelling of physical processes. You will develop knowledge and understanding of a variety or relevant numerical techniques and learn how to efficiently implement them in C++.

Statistical Machine Learning

Machine Learning is a topic at the interface between statistics and computer science that concerns models that can adapt to and make predictions based on data. This module builds on principles of statistical inference and linear regression. It introduces a variety of methods of regression and classification, trade-off, and on methods to measure and compensate for overfitting.

You will benefit with hands-on learning using computational methods to tackle challenging real world machine learning problems.

Topics in Biomedical Mathematics

This module illustrates the applications of advanced techniques of mathematical modelling using ordinary and partial differential equations. A variety of medical and biological topics are covered bringing you closer to active fields of mathematical research.

Time Series and Forecasting

This module will provide you with a general introduction to the analysis of data that arise sequentially in time. You will discuss several commonly-occurring models, including methods for model identification for real-time series data. You will develop techniques for estimating the parameters of a model, assessing its fit and forecasting future values.

Uncertainty Quantification

You will learn to apply ideas from probability and statistics and various mathematical tools in traditional areas of applied and computational mathematics. There will be a focus on ordinary differential equation (ODE) and partial differential equation (PDE) models. The module will provide an introduction to a variety of techniques which are useful in Uncertainty Quantification and will concentrate on a more in-depth study of selected application areas.

The above is a sample of the typical modules we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Modules (including methods of assessment) may change or be updated, or modules may be cancelled, over the duration of the course due to a number of reasons such as curriculum developments or staffing changes. Please refer to the module catalogue for information on available modules. This content was last updated on

Fees and funding

UK students

Per year

International students

Per year

*For full details including fees for part-time students and reduced fees during your time studying abroad or on placement (where applicable), see our fees page.

If you are a student from the EU, EEA or Switzerland, you may be asked to complete a fee status questionnaire and your answers will be assessed using guidance issued by the UK Council for International Student Affairs (UKCISA) .

Additional costs

All students will need at least one device to approve security access requests via Multi-Factor Authentication (MFA). We also recommend students have a suitable laptop to work both on and off-campus. For more information, please check the equipment advice.

As a student on this course, you should factor some additional costs into your budget, alongside your tuition fees and living expenses.


You should be able to access most of the books you’ll need through our libraries, though you may wish to purchase your own copies.


Due to our commitment to sustainability, we don’t print lecture notes but these are available digitally. 

Industrial placement year

For the year in industry, you may be paid but you will need to factor in accommodation or travel costs. 


To support your studies, the university recommends you have a suitable laptop to work on when on or off campus. If you already have a device, it is unlikely you will need a new one in the short term. If you are looking into buying a new device, we recommend you buy a Windows laptop, as it is more flexible and many software packages you will need are only compatible with Windows.

Although you won’t need a very powerful computer, it is wise to choose one that will last. The University has prepared a set of recommended specifications to help you choose a suitable laptop.

If you are experiencing financial difficulties and you are struggling to manage your costs, the Hardship Funds may be able to assist you.

Scholarships and bursaries

School scholarships

We offer an international orientation scholarship of £2,000 to the best international (full-time, non EU) applicants on this course.

It will be paid at most once for each year of study. If you repeat a year for any reason, the scholarship will not be paid for that repeated year. The scholarship is awarded in subsequent years to students who perform well academically (at the level of a 2:1 Hons degree or better at the first attempt). 

The scholarship will be paid in December each year provided you have:

  • completed your registration
  • been recorded as a student on a relevant course in the 1 December census
  • paid the first instalment of your fee

Home students*

Over one third of our UK students receive our means-tested core bursary, worth up to £1,000 a year. Full details can be found on our financial support pages.

* A 'home' student is one who meets certain UK residence criteria. These are the same criteria as apply to eligibility for home funding from Student Finance.

International students

We offer a range of international undergraduate scholarships for high-achieving international scholars who can put their Nottingham degree to great use in their careers.

International scholarships


Mathematics is a broad and versatile subject leading to many possible careers. Skilled mathematicians are found in a variety of organisations, in lots of different sectors.

As this is a new degree programme based on the main MMath course, our students are yet to graduate. Our standard MMath graduates are helping to shape the future in many sectors including data analysis, finance and IT. Many work in science, engineering or consultancy, others pursue careers within government departments. Some graduates choose a career in mathematical research.

The knowledge and skills that you will gain during this degree, can typically lead to roles working as:

  • Actuarial analyst
  • Data analyst
  • Financial analyst
  • Junior software consultant
  • Leading aircraft engineering technician
  • Maths teacher
  • Mathematical researcher
  • Tax consultant
  • Trainee operational meteorologist

Read our alumni profiles for the sort of jobs our graduates go on to do.

Other opportunities to help your employability

Become a PASS leader in your second or third year. Teaching first-year students reinforces your own mathematical knowledge. It develops communication, organisational and time management skills which can help to enhance your CV when you start applying for jobs

The Nottingham Internship Scheme provides a range of work experience opportunities and internships throughout the year

The Nottingham Advantage Award is our free scheme to boost your employability. There are over 200 extracurricular activities to choose from

Average starting salary and career progression

86.8% of undergraduates from the School of Mathematical Sciences secured graduate level employment or further study within 15 months of graduation. The average annual salary for these graduates was £27,295.*

* Data from University of Nottingham graduates, 2017-2019. HESA Graduate Outcomes. Sample sizes vary. The average annual salary is based on graduates working full-time within the UK.

Studying for a degree at the University of Nottingham will provide you with the type of skills and experiences that will prove invaluable in any career, whichever direction you decide to take.

Throughout your time with us, our Careers and Employability Service can work with you to improve your employability skills even further; assisting with job or course applications, searching for appropriate work experience placements and hosting events to bring you closer to a wide range of prospective employers.

Have a look at our careers page for an overview of all the employability support and opportunities that we provide to current students.

The University of Nottingham is consistently named as one of the most targeted universities by Britain’s leading graduate employers (Ranked in the top ten in The Graduate Market in 2013-2020, High Fliers Research).

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Important information

This online prospectus has been drafted in advance of the academic year to which it applies. Every effort has been made to ensure that the information is accurate at the time of publishing, but changes (for example to course content) are likely to occur given the interval between publishing and commencement of the course. It is therefore very important to check this website for any updates before you apply for the course where there has been an interval between you reading this website and applying.